110602 How Many Pieces of Land

// Max =  1 + C(n, 2) + C(n, 4)// Refer to http://en.wikipedia.org/wiki/Dividing_a_circle_into_areas or  // http://www.arbelos.co.uk/Papers/Chords-regions.pdf #include <vector>#include <iostream>#include <string.h>using namespace std;class Integer{public:Integer(char* buf, int len){for (int i = 0; i < len; ++i)m_data.push_back(buf[i] - '0');}Integer() {}void Print(){int cnt = m_data.size();if (cnt <= 0)cout << "0";for (int i = 0; i < cnt; ++i)cout << m_data[i];}void Add(const Integer& other, Integer& result) const{result.m_data.clear();int flag = 0;int i = 0, limit = (other.m_data.size() > m_data.size()) ? other.m_data.size() : m_data.size();while(i < limit){int num1 = (i < m_data.size()) ? m_data[m_data.size() - 1 - i] : 0;int num2 = (i < other.m_data.size()) ? other.m_data[other.m_data.size() - 1 - i] : 0;int sum = num1 + num2 + flag;flag = sum / 10;result.m_data.push_back(sum % 10);++i;}if (flag > 0)result.m_data.push_back(flag);result.ShrinkAndInvert();}void Minus(const Integer& other, Integer& result) const{result.m_data.clear();int flag = 0;int i = 0, limit = (other.m_data.size() > m_data.size()) ? other.m_data.size() : m_data.size();while(i < limit){int num1 = (i < m_data.size()) ? m_data[m_data.size() - 1 - i] : 0;int num2 = (i < other.m_data.size()) ? other.m_data[other.m_data.size() - 1 - i] : 0;int left = num1 - flag - num2;if (left < 0){flag = 1;left += 10;}elseflag = 0;result.m_data.push_back(left);++i;}if (flag < 0)result.m_data.push_back(9);result.ShrinkAndInvert();}void Multiply(const Integer& other, Integer& result) const{result.m_data.clear();for (int i = other.m_data.size() - 1; i >= 0; --i){Integer tmp, sum;Multiply(other.m_data[i], tmp, other.m_data.size() - i - 1);result.Add(tmp, sum);result = sum;}}void Multiply(const int n, Integer& result, int shift) const{result.m_data.clear();for (int i = 0; i < shift; ++i)result.m_data.push_back(0);int flag = 0;for (int i = m_data.size() - 1; i >= 0; --i){int tmp = m_data[i] * n + flag;flag = tmp / 10;result.m_data.push_back(tmp % 10);}if (flag > 0)result.m_data.push_back(flag);result.ShrinkAndInvert();}void Divide(const Integer& other, Integer& result) const{result.m_data.clear();if (operator == (other)){result.m_data.push_back(1);return;}if (!(operator > (other)))return;int sizeDev = m_data.size() - other.m_data.size();Integer tmp = (*this);Integer resultTmp1, resultTmp2;for (int i = sizeDev; i >= 0; --i){Integer tmp1, tmp2;other.Multiply(1, tmp1, i);int sum = 0;while(true){if (tmp >= tmp1){tmp.Minus(tmp1, tmp2);++sum;tmp = tmp2;}elsebreak;}resultTmp1.m_data.clear();if (sum > 0){for (int j = 0; j < i; ++j)resultTmp1.m_data.push_back(0);resultTmp1.m_data.push_back(sum);resultTmp1.ShrinkAndInvert();}result.Add(resultTmp1, resultTmp2);result = resultTmp2;}}private:void ShrinkAndInvert(){while(m_data.size() != 0){if (m_data[m_data.size() - 1] == 0)m_data.pop_back();elsebreak;}int cnt = m_data.size();for (int i = 0; i < cnt / 2; ++i){int tmp = m_data[i];m_data[i] = m_data[cnt - 1 - i];m_data[cnt - 1 - i] = tmp;}}bool operator > (const Integer& other) const{if (m_data.size() > other.m_data.size())return true;if (m_data.size() < other.m_data.size())return false;for (int i = 0; i < m_data.size(); ++i)if (m_data[i] < other.m_data[i])return false;else if (m_data[i] > other.m_data[i])return true;return false;}bool operator == (const Integer& other) const{if (m_data.size() != other.m_data.size())return false;for (int i = 0; i < m_data.size(); ++i)if (m_data[i] != other.m_data[i])return false;return true;}bool operator >= (const Integer& other) const{return ((operator > (other)) || (operator == (other)));}private:vector<int> m_data;};static void DoTest(char* data){if ((!data) || (data[0] == '\0')){cout << 0 << endl;return;}if (data[1] == '\0'){int max = -1;if (data[0] == '0')max = 1;else if (data[1] == '1')max = 1;else if (data[2] == '2')max = 2;else if (data[3] == '3')max = 8;if (max > 0){cout << max << endl;return;}}Integer num(data, strlen(data));Integer one("1", 1);Integer two("2", 1);Integer three("3", 1);Integer four("4", 1);Integer result, tmpResult1, tmpResult2, tmpResult3, cn2, cn4;Integer numMinus1;num.Minus(one, numMinus1);num.Multiply(numMinus1, tmpResult1);tmpResult1.Divide(two, cn2); // Now we have C(n, 2)num.Minus(two, tmpResult1);cn2.Multiply(tmpResult1, tmpResult2);num.Minus(three, tmpResult1);tmpResult2.Multiply(tmpResult1, tmpResult3);tmpResult3.Divide(three, tmpResult2);tmpResult2.Divide(four, cn4);one.Add(cn2, tmpResult1);tmpResult1.Add(cn4, result);result.Print();cout << endl;}#define MAX_BUF_SIZE 4096static void Test(){int cnt;char buf[MAX_BUF_SIZE];cin >> cnt;for (int i = 0; i < cnt; ++i){cin >> buf;DoTest(buf);}}int main(int argc, char* argv[]){Test();return 0;}